- Series
- CDSNS Colloquium
- Time
- Monday, March 26, 2012 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Predrag Cvitanovic – Georgia Tech, Physics
- Organizer
- Rafael de la Llave
With recent advances in experimental imaging, computational methods,
and dynamics insights it is now possible to start charting out the
terra incognita explored by turbulence in strongly nonlinear classical
field theories, such as fluid flows. In presence of continuous
symmetries these solutions sweep out 2- and higher-dimensional
manifolds (group orbits) of physically equivalent states,
interconnected by a web of still higher-dimensional stable/unstable
manifolds, all embedded in the PDE infinite-dimensional state spaces.
In order to chart such invariant manifolds, one must first quotient the
symmetries, i.e. replace the dynamics on M by an equivalent, symmetry
reduced flow on M/G, in which each group orbit of symmetry-related
states is replaced by a single representative.Happy news: The
problem has been solved often, first by Jacobi (1846), then by Hilbert
and Weyl (1921), then by Cartan (1924), then by [...], then in this
week's arXiv [...]. Turns out, it's not as easy as it looks.Still,
every unhappy family is unhappy in its own way: The Hilbert's solution
(invariant polynomial bases) is useless. The way we do this in quantum
field theory (gauge fixing) is not right either. Currently only the
"method of slices" does the job: it slices the state space by a set of
hyperplanes in such a way that each group orbit manifold of
symmetry-equivalent points is represented by a single point, but as
slices are only local, tangent charts, an atlas comprised from a set of
charts is needed to capture the flow globally. Lots of work and not a
pretty sight (Nature does not like symmetries), but one is rewarded by
much deeper insights into turbulent dynamics; without this atlas you
will not get anywhere.This is not a fluid dynamics talk. If you
care about atomic, nuclear or celestial physics, general relativity or
quantum field theory you might be interested and perhaps help us do
this better.You can take part in this seminar from wherever you are by clicking onevo.caltech.edu/evoNext/koala.jnlp?meeting=M2MvMB2M2IDsDs9I9lDM92